Question

An infinite GP has first term x and sum 5, then x belongs to (a) x < -10 (b) -10 < x < 0 (c) 0 < x < 10 (d) x > 10

Answer 1

Answer:

Step-by-step explanation:

Hi my friend,

Infinite GP sum formula = ar + ar² + ar³ + .........

Where a is the first term and r is the common ratio

If |r| < 1, the sum converges to

$S_{Infinity } = \frac{a}{1-r}$

If |r| > 1, the sum doesn't exist and series diverges.

Given:

First term = a = x

$S_{Infinity} = 5$

Hence from the equation of |r| < 1,

$S_{Infinity} = \frac{x}{1-r}\\=> 5 = \frac{x}{1-r}\\=> 5 - 5r = x\\=> -5r = x - 5\\=> 5r = 5 - x\\=> r = \frac{5 - x}{5}$

But as |r| < 1,

The equation now will be

$-1 <\frac{5 - x}{5} < 1\\=> -5 < 5 - x < 5\\=> -5 -5 < -x < 5 - 5\\=> -10 < -x < 0\\=> 10 > x > 0\\=> 0 < x < 10$

Hence option (c) is right option.

Thanks.

Harith

Maths Aryabhatta

Answer 2

Answer:

hey mate...... down there is your answer

Step-by-step explanation:

please mark as brainlist answer